dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter the answer in terms of t. dz || dt

Q: Show that the 2-D Heat Equation dx² ди becomes ди if x = es cos w and y = es sin w. You ma dt dy?…

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Q: Determine the Solutions of ke followsing differential eguation ě (5-x) dx Xy dy %3D

A: A separable differential equation is any equation that can be written in the form. y′=f(x)g(y). The…

Q: Find the general solution of the differential cquations : d2y = e2* (12 cos 3x – 5 sin 3x) dx2 2.…

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Q: b) Use the Laplace Transform to solve the following differential equation given the initial…

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (- 0.01) xe…

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Q: 14. Solve the equation d?x 3 +2x sin dt2 dt dx given that at t = 0, x = 0 and 1. dt nent

A: See the details solution in below

Q: The order and degree of the partial differential equation respectively 6 9. dz + sin x = xy? is_ %3D

A: Given,          ∂4z∂x46+∂z∂x9+sinx=xy2

Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: Q1-Use the chain rule to express dy / dx in terms of xand y: 1-1 a) y = аnd x = at 1= 2 1+1 b) y=1-…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Solve the initial - value problem : dy = Cos x - Sinx +y, 0 sx < 0.5 , y(0) = 0 dx using (a) four-th…

A: Given differential equation                                                dydx=cosx-sinx+y,…

Q: Q:- solve the differential equation by Laplace transform : y" – 3y' + 2y = e3t %3D Where the initial…

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Q: Solve the partial differential equation of a²u = 6xt? + 3sin(t) + e¬*cos(t), subject to the boundar…

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Q: d3x 2. Verify that sin kt is a solution of the equation in + k3x = 0 %3D dt3

A: Explanation of the answer is as follows

Q: dy Find the particular solution of 2y- = x+ sin a when y (0) = 1

A: we have to integrate both side , we get

Q: The differential equation is as follows: d[RL] -[RL]k2 dt with initial conditions, [RL], = [RL];=0…

A: So, we will have to use [ RL ]0  as a value in here, and hence, it will be treated as a constant.…

Q: 4. Given y = 3u² – u and u = x³ – 1, use the Chain Rule in Leibniz notation to find the value of dy…

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Q: The exact differential d(xy)= xdy+ ydx , what is the d O= 4x²y°dy+ 2xy*dx.

A: Find your answer below

Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: -cosh(x)dx 18) St?cos(2t)dt S 2y²e»*dy 19) Sxeax+1dx dx Sx²e2*dx 20) S x-x2 ) (2?/ª x)°e-In(x²)e3×dx…

A: We have to find the integration.

Q: If y(x) satisfies the differential equation y" + x²y = 0, where y(0) = yo and y'(0) = y, show that…

A: since we know that L[y''] = p2Y(s)-py(0)-y(0)

Q: find the integrating factor of the given linear DE and general solution of the y'+1/x (y)=cos(x)

A: Consider the given linear differential equation. y'+1xy=cosx The objective of the problem is to find…

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute y'…

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Q: O1 Find: fx³ cos x dx using Integration by parts b. ſ cosx? 2x dx using Substitution Method a.

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Q: Find the particular solution of (cos x – x sin x + y²) dx + 2xy dy = 0 that satisfies the initial…

A: Make the absolute form and solve this differential equation.

Q: dx +4x = 2e 3 , x(0)= 5 dt (d) dx +4x = sin 2t , x(0)= 0 dt (e)

A: Laplace transferom, solve the differential equation by using Laplace transferom

Q: (b) Find the general solútion of the differential equation d'y dy 2 +y x+1 dx - dx2 without using…

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Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: Find the differential dy of the given functions . (Use "dx" for dx.) a) y = 2x − (sin(x))2 b)…

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Q: Let y = tan x. (a) Find the differential dy. (b) Evaluate dy and Δy if x = π/3 and dx = -0.2…

A: Let,  y=fanxa To find differential dy, differentiate y       with respect to x,        dy=sec2x dx

Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

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Q: Find the singular sol" of the differential eqh (P+1)² (y-px) = 1 -

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Q: dx 2а — У dt fip dt x + 2 cos(t)

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

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Q: Use the Laplace transform to solve the differential equation dy x – 2y dx with the initial condition…

A: Solved below

Q: dy The integrating factor of Linear differential equations + y x 4tan ¤ = sec²x is_ dx In cos 4x tan…

A: The coefficient of y is: P=4tanx So the integrating factor is: e∫Pdx

Q: dy 1- Solve = cos x + y, where y = dx 2.0 at x 0 take step size h = Ax=

A: Given,         dydx=cosx+y Where y=2.0  at x=0   and h=0.1

Q: dx + 3x dt cos(5t) %3D with x(0) = 1. x(t) = %3D

A: The given initial value problem is: dxdt+3x=cos(5t) ;         x(0)=1

Q: df Q4) A) Find dx by using chain rule if f = , u=-1 , x=-1 u+1 B) Evaluate the following integral:…

A: A) To find the derivative of the given function f=u-1u+12 with u=1x2-1

Q: Solve the following differential equation given the initial value. dy = tan(x), y(0) =1 dx A y = In|…

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Q: Given y = 4e* + In x, find the differential dy. %3D

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Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: Let y = y(t) be the solution to the initial value problem dy = e' cos t; y(0) = 1. - dt Find the…

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Q: Let y = tan(4r + 4). Find the differential dy when x = 1 and dæ 0.4 Find the differential dy when x…

A: Given that, y=tan4x+4 differentiating both sides with respect to x, we get…

Q: Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Given  data  xey+2z-cos(xy)+ey-ln2=4  ,  A(ln2,0) Also given  when x changes by (dx=0.01) and y…

Q: Find the general solution of the nonhomogeneous 2nd order ODE (Use the appropriate method) y" - 4y'…

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Q: 3 a) Find the exact integer value of a for which tsin (at)dt == ft sin (xt) dt = -². where a1. T

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Q: äbäi 14 Q) Use the chain rule to express dy / dx in terms of x :and y for the following y = 1- t 1…

A: Given y=1-1tt=11-x Thus dydt = ddt1-1t= ddt(1)-ddt1t= 0--1t2= 1t2 and dtdx = ddx11-x=…

Q: 3. Find dy, where; (x+y) = 2 a) cos (xy)- + e b) e+ iPtany=1 , u= xlax (use chain rule)

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Q: THE IVP

A: Consider the provided differential equation with initial condition is,

Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…